Question

Please help and provide an explanation for why the answer is f(x) = 3/2x + 7

Answer 1

Answer:

$y=\frac{3}{2}x+7$

Step-by-step explanation:

To write the equation of a line, two information are needed.

1. Slope (also known as gradient)
2. A pair of coordinates (or a point) on the line

The slope can be calculated using the gradient formula as long as two pairs of coordinates are given. This question provides the slope, hence we can substitute its value into the equation right away.

In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept. The slope gives us the steepness of the line, while the y-intercept is the y value in which the line cuts through the y-axis (vertical axis).

y= mx +c

Given that slope= $\frac{3}{2}$, m= $\frac{3}{2}$.

Substitute the value of m:

$y=\frac{3}{2}x+c$

Next, find the value of c by substituting a pair of coordinates.

When x= -4, y= 1,

$1=\frac{3}{2} (-4)+c$

1= -6 +c

Add 6 to both sides:

c= 1 +6

c= 7

Substituting the value of c:

$\bf{y=\frac{3}{2}x +7 }$

For more examples on writing equation of lines, check out: brainly.com/question/27941697

Answer 2

Answer:

see below

Step-by-step explanation:

the point-slope equation is

y-1 = 3/2 (x+4)