zero

y = mx + b, where m is the slope and b is the y-intercept. Slope-intercept is the form used most often as the simplified equation of a line….index: subject areas.

The standard form of such an equation is Ax + By + C = 0 or Ax + By = C. When you rearrange this equation to get y by itself on the left side, it takes the form y = mx +b. This is called slope intercept form because m is equal to the slope of the line, and b is the value of y when x = 0, which makes it the y-intercept.

The slope-intercept form is y=mx+b y = m x + b , where m is the slope and b is the y-intercept. Using the slope-intercept form, the y-intercept is 3 .

y=3 would be nothing more than a horizontal line through y=3. So the rise is always 0 (it never goes up or down) and the run is always the distance from zero to any point on the line. In other words, the slope would be 0/the change in x, which is always 0.

y-intercept: Put x = 0 in the equation y = 2x – 6 and solve for x. The y-intercept is -6.

The y-intercept of y=-2x+6 equals 6.

In this equation, y = 2x – 5, it is already in that form and so the cumber in front of the x is the slope (2) and the constant number is the y-intercept (-5) – it’s negative because of the minus sign in front of the number. So, the slope is 2 and the y-intercept is -5.

The ordered pairs (3, 0) and (0, -6) are solutions of 2x – y = 6. Graphing these points and connecting them with a straight line give us the graph of 2x – y = 6.

To graph y=2x−6 you would plot a point at (0,−6) at the y-intercept, then go up 2 over 1 since the slope is 2 (same as 21 ). You would continue from that point going up 2 right 1 plotting points at each stop and then you can draw the line.

Ordered pair is (2, -7/5) .

Ordered pairs (x,y) that work in both equations are called solutions to the system of equations. They represent the intersection points of the two lines. Thus a system has one solution, no solutions, or infinitely many solutions. If an ordered pair is a solution, it must work in both equations.

x = 0 : y = 0 + 4 → y = 4 is the y-intercept.

The line y=3 is a horizontal line, and a horizontal line has a slope of zero. The only lines parallel to a horizontal line are other horizontal lines. Therefore, there is no slope.

To write a slope-intercept equation from a graph, find the point where the graph crosses the y-axis, b, and the slope, m, and plug them into the equation y=mx+b.

Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept). Watch this video to learn more about it and see some examples.

Examples of Applying the Concept of Point-Slope Form of a Line. The slope is given as m = 3 m = 3 m=3, and the point (2,5) has coordinates of x 1 = 2 {x_1} = 2 x1=2 and y 1 = 5 {y_1} = 5 y1=5. Now plug the known values into the slope-intercept form to get the final answer.