Graphing help Write the equation in slope-intercept form.

[Guest]

Find the equation of the line shown in the graph. Write the equation in slope-intercept form.

Study material images attached for 3 solutions.

[Guest]

https://www.math10.com/en/math-games/ma ... lines.html

Select Slope-Intercept

[Guest]

Do you understand what "slope- intercept" means?
The slope-intercept equation for a line is "y= ax+ b"

"b" is the "y-intercept" because when x= 0, y= a(0)+ b= b, the y value where the line crosses ("intercepts") the y-axis.

Do you know what the slope is?
If two points are $(x_0, y_0)$ and $(x_1, y_1)$ are two points on the line then the slope is $\frac{y_1- y_0}{x_1- x_0}$. That is the tangent of the angle the line makes with x-axis so measure how much the line slopes.'

So look at these graphs. What is the y-value where the line crosses the x- axis?
Choose two points on each line and calculate $\frac{y_1- y_0}{x_1- x_0}$.

[Guest]

For example, I see that the first graph crosses the y-axis at (0, . The '"b" in "y= ax+ b" is 8.

While you could use any two points to calculate the slope, on a graph like this, integer values are easier to recognize. I have already said that the graph goes through (0, 8 ). It also goes through (4, 3). Taking $(x_1, y_1)= (0, 8 )$ and $(x_2, y_2= (4, 3)$ the slope is $\frac{3- 8}{4- 0}= \frac{-5}{4}= -\frac{5}{4}$. The "slope-intercept form" for this graph is $y= -\frac{5}{4}x+ 8$.

(Notice that choosing $(x_1, y_1)= (4, 3)$ and $(x_2, y_2)= (0, 8 )$ only changes the sign in both numerator and denominator and so does not change the fraction: $\frac{8- 3}{0- 4}= \frac{5}{-4}= -\frac{5}{4}$.)