Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

To find the slope of the given line we need to get the line into slope-intercept form (y = mx + b), which means we need to solve for y: The slope of the line 4x – 5y = –10 is m = 4/5. Therefore, the slope of the line perpendicular to this line would have to be m = –5/4.

Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.

Correct answer: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.

The slope of a perpendicular line to a vertical line is zero.

So the slope perpendicular to 3/5 is -5/3. Perpendicular lines have negative reciprocal slopes. That means the fraction is flipped and multiplied by negative 1. So if one line has a slope of 3/5, then a line perpendicular to it has a slope of -5/3.

Correct answer: The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite: in this case to 3. Then find the reciprocal by switching the denominator and numerator to get 1/3; therefore the slope of the perpendicular line is 1/3.

As mentioned above, parallel lines have the same slope. So, if we know the slope of the line parallel to our line, we have it made.

There are three steps in calculating the slope of a straight line when you are not given its equation.

1. Step One: Identify two points on the line.
2. Step Two: Select one to be (x1, y1) and the other to be (x2, y2).
3. Step Three: Use the slope equation to calculate slope.

In general, the slope intercept form assumes the formula: y = mx + b.

1. M is the slope (lesson on slope) Mnemonic : ‘m’ means ‘move’
2. B is the y-intercept (lesson on the y-intercept) Mnemonic: ‘b’ means where the line begins.

Standard form is another way to write slope-intercept form (as opposed to y=mx+b). It is written as Ax+By=C. You can also change slope-intercept form to standard form like this: Y=-3/2x+3. A, B, C are integers (positive or negative whole numbers) No fractions nor decimals in standard form. …

The slope-intercept form of a linear equation is where one side contains just “y”. So, it will look like: y = mx + b where “m” and “b” are numbers. This form of the equation is very useful. The coefficient of “x” (the “m” value) is the slope of the line.

In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the “slope-intercept form”.

Slope-intercept form, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.

When a word problem involves a constant rate or speed and a beginning amount, it can be written in slope-intercept form: y=mx+b. To do this, recognize which number will represent m, the rate, and which number will represent b, the y-intercept.

Slope intercept form of a linear equation is y = mx+b, where m is the slope and b is the y-intercept.

Some real life examples of slope include: in building roads one must figure out how steep the road will be. skiers/snowboarders need to consider the slopes of hills in order to judge the dangers, speeds, etc. when constructing wheelchair ramps, slope is a major consideration.

Word Problems involving Linear Equations

1. Read the problem carefully and in its entirety. You have no idea how many times this step is missed.
2. Write a linear equation based on the information given. This involves what we just went over.
3. Solve the equation.
4. Check your answer to see if it makes sense.

Steps For Solving Real World Problems

1. Highlight the important information in the problem that will help write two equations.
2. Define your variables.
3. Write two equations.
4. Use one of the methods for solving systems of equations to solve.
5. Check your answers by substituting your ordered pair into the original equations.