Answer:
9) [tex]y=\frac{2}{5} x+4[/tex]
10) [tex]y=4x-5[/tex]
Step-by-step explanation:
Slope-intercept form is [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept, or the value of y when the line crosses the y-axis.
Question 9
[tex]y=mx+b[/tex]
The question tells us that the slope of the line is [tex]\frac{2}{5}[/tex]. Because the slope is [tex]m[/tex], plug [tex]\frac{2}{5}[/tex] into the equation as [tex]m[/tex].
[tex]y=\frac{2}{5} x+b[/tex]
Then, it tells us that the y-intercept is (0,4). Recall that the y-intercept is the value of y when the line crosses the y-axis. The value of y in the point (0,4) is 4. Because the y-intercept is [tex]b[/tex], plug 4 into the equation as [tex]b[/tex].
[tex]y=\frac{2}{5} x+4[/tex]
Question 10
[tex]y=mx+b[/tex]
First, we must calculate the slope using the slope equation:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] when the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
The given points are (0,-5) and (2,3). Plug those into the equation.
[tex]\frac{3-(-5)}{2-0}[/tex]
Two negatives make a positive
[tex]= \frac{3+5}{2-0}\\= \frac{8}{2} \\= 4[/tex]
Therefore, the slope of the line is 4. Plug 4 into the original equation as [tex]m[/tex].
[tex]y=4x+b[/tex]
Now, we can find the y-intercept by simply looking at the graph. The line crosses the y-axis at the point (0,-5). Therefore, the y-intercept is -5. Plug -5 into the equation as [tex]b[/tex].
[tex]y=4x+(-5)\\y=4x-5[/tex]
I hope this helps!
