Question

Please I need help!

Answer 1

Answer:

1)

$\text{ Slope = -3}$

2)

$y+4=-\frac{7}{8}(x-7)$

3)

$y=-\frac{7}{8}x+\frac{17}{8}$

Step-by-step explanation:

We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.

1)

First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:

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

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:

$m=\frac{3-(-4)}{-1-7}$

Subtract. So, our slope is:

$m=\frac{7}{-8}=-7/8$

2)

Now, let's use the point-slope form:

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

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:

$y-(-4)=-\frac{7}{8}(x-7)$

Simplify. So, our point-slope equation is:

$y+4=-\frac{7}{8}(x-7)$

3)

Finally, we want to convert this into slope-intercept form. So, let's solve for our y.

On the right, distribute:

$y+4=-\frac{7}{8}x+\frac{49}{8}$

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:

$y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}$

Subtract. So, our slope-intercept equation is:

$y=-\frac{7}{8}x+\frac{17}{8}$

And we're done!

Answer 2

Answer: Shown Below

Step-by-step explanation:

1. -7/8

2. y+4= (-7/8)(x-7)

3. y=(-7/8)x+ (17/8)

Just did it