Answer:
[tex]y=\frac{-2}{3} x+1[/tex]
Step-by-step explanation:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex]. Here's what the variables mean:
y = the y-coordinate
m = the slope
x = the x=coordinate
b = the y-intercept (what y is equal to when the line crosses the y-axis)
First, we need to calculate the slope of the line (m). The slope is the [tex]\frac{rise}{run}[/tex] of the line, or in other words, the change in y over the change in x. We can find this by just looking at the graph, between the two given points. For 3 spaces the line travels to the right, it travels downward 2 spaces. Therefore, the slope of the line is [tex]\frac{-2}{3}[/tex].
We can also calculate this using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] by using two points that fall on the line, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. Here, we can use the points (-3,3) and (0,1).
[tex]\frac{y_2-y_1}{x_2-x_1}\\\frac{1-3}{0-(-3)}[/tex]
Two negatives make a positive
[tex]=\frac{1-3}{0+3}\\=\frac{-2}{3}[/tex]
Then, we need to find the y-intercept of the line (b). We can find this by, again, looking at the graph. The line crosses the y-axis when y is equal to 1, so the y-intercept of the line is 1.
Now, we plug our calculated values back into the original equation:
[tex]y=mx+b\\y=\frac{-2}{3} x+1[/tex]
I hope this helps!
