Question

A line passes through the point (1, - 6) and has a slope of 8. Write an equation in slope-intercept form for this line.

Answer 1

Answer:

y=8x-14

Step-by-step explanation:

Hi there!

We want to write the equation of the line that passes through (1, -6) and has a slope of 8 in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope (8), we can immediately plug that into the equation

So far, the equation of the line is:

y=8x+b

Now we need to find b

The line passes through the point (1, -6), which means that the point is a solution to the equation; when plugged into the equation, it'll create a true statement. This can help us find unknown variables, like b

Substitute 1 as x and -6 as y in the equation to solve for b

-6=8(1)+b

Multiply

-6=8+b

Subtract 8 from both sides

-14=b

Substitute -14 as b into the equation

y=8x-14

Hope this helps!

Answer 2

Answer:

$\boxed {\boxed {\sf y=8x-14}}$

Step-by-step explanation:

We are asked to find the equation of a line in slope-intercept form. We are given a point and a slope, so we can use the point-slope formula.

$y-y_1= m(x-x_1)$

In this formula, m is the slope and (x₁, y₁) is the point the line passes through. The slope of the line is 8 and it passes through the point (1, -6). Therefore,

• m= 8
• x₁= 1
• y₁= -6

Substitute these values into the formula.

$y- (-6) = 8(x-1)$

Remember that 2 back to back subtraction signs are the same as an addition sign.

$y+6=8(x-1)$

The line must be in slope-intercept form or y=mx+b (m is the slope and b is the y-intercept. We must isolate the variable y on one side of the equation. First, distribute on the right side of the equation. Multiply each term inside the parentheses by 8.

$y+6 = (8*x) + (8*-1)$

$y+6= (8x)+ (-8)$

$y+6=8x-8$

6 is being added to y. The inverse operation of addition is subtraction, so we subtract 6 from both sides of the equation.

$y+6-6=8x-8-6$

$y=8x-8-6$

$y= 8x-14$

The equation of the line in slope-intercept form is y=8x-14. The slope is 8 and the y-intercept is -14.