Question

Please help

Answer 1

Answer:

$\displaystyle \large{y = \frac{1}{4} x + 1}$

Step-by-step explanation:

Whenever you solve a word problem, our first step is to read and gather the information we find.

"A line intersects the point (-8,-1) and has a slope of 1/4. What is the slope-intercept equation for this line?"

After reading the question, I am going to highlight or bold the contexts that are important to our problem-solving.

"A line intersects the point (-8,-1) and has a slope of 1/4. What is the slope-intercept equation for this line?"

First, let's understand that slope-intercept equation is in the form of y = mx+b where m = slope and b = y-intercept

After reading the context, what do we know?

• a slope of 1/4
• a line passes through (-8,-1)
• write in slope-intercept form

We finally have the information — our first step is to write our slope-intercept equation.

$\displaystyle \large{y = mx + b}$

We know that m is slope which is 1/4 — substitute in the equation.

$\displaystyle \large{y = \frac{1}{4} x + b}$

We have used the two information which are a slope of 1/4 and slope-intercept equation.

That only leaves to one information which is a line that passes through (-8,-1).

Since the graph has to pass through the point, we substitute x = -8 and y = -1.

$\displaystyle \large{ - 1= \frac{1}{4} ( - 8)+ b}$

After using all information, it seems that we are solving for b-term or y-intercept.

$\displaystyle \large{ - 1= \frac{1}{1} ( - 2)+ b}$

From above — cross-division.

$\displaystyle \large{ - 1= 1( - 2)+ b} \\ \displaystyle \large{ - 1= - 2+ b}$

Add both sides by 2 to isolate b-term.

$\displaystyle \large{ - 1 + 2= - 2 + 2+ b} \\ \displaystyle \large{ 1= b}$

Therefore, the value of b is 1. From the equation:

$\displaystyle \large{y = \frac{1}{4} x + b}$

Substitute b = 1 in the equation.

$\displaystyle \large{y = \frac{1}{4} x + 1}$

And we're done!