Question

Equations, graphs, Slopes and y-intercepts : application

Answer 1

Answer:

$y=\frac{1}{2}x-5$

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = slope

$m=\frac{y_2-y_1}{x_2-x_1}$

To find slope, we use points on the line.

Here, I will be suing (-6, -8) and (8, -1)

$m=\frac{1-(-8)}{8-(-6)} \\\\m=\frac{-1+8}{8+6} \\\\m=\frac{7}{14}\\\\m=\frac{1}{2}$

$y=mx+b$

$y=\frac{1}{2} x+b$

Now, we use either of our points (-6, -8) OR (8, 1) to find b.

I will be using (8, -1):

$y=\frac{1}{2}x+b\\\\-1=\frac{1}{2}(8)+b\\\\-1=4+b\\\\-4-4\\\\-5=b$

$y=\frac{1}{2}x+b== > y=\frac{1}{2}x-5$

Check your answer manually: (-6, -8)

$y=\frac{9}{14}x-\frac{29}{7}\\\\-8=\frac{9}{14}(-6)-\frac{29}{7}\\\\-8=\frac{9}{7}(-3)-\frac{29}{7}\\\\-8=-\frac{27}{7}-\frac{29}{7}\\\\-8=-\frac{56}{7}\\\\-8=-8$

This statement is correct.

*You can also view the attached graph to verify the answer, meaning that those two points should lie on the same line.*

Hope this helps!

Answer 2

Answer:

$\sf y= \dfrac{1}{2}x-5$

Explanation:

• coordinates taken: (0, -5), (6, -2)

slope:

$\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}$

$\rightarrow \sf \dfrac{-2--5}{6-0}$

$\rightarrow \sf \dfrac{1}{2}$

equation in slope intercept form:

• y = m(x) + b                          [ where "m is slope", "b is y-intercept" ]

$\sf y= \dfrac{1}{2}x-5$