Question

Write an equation of the line that passes through the point 3, -2 and has a slope of -3

Answer 1

y = -3x + 7

Explanation:

Pre-Solving

We are given that a line passes through the point (3, -2) and has a slope of -3.
We want to write the equation of this line, and there are three ways to do so:

• Slope-intercept form, which is y=mx+b where m is the slope and b is the value of y at the y-intercept.
• Standard form, which is ax+by=c where a, b, and c are free integer coefficients.
• Slope-point form, which is
  `y-y_1=m(x-x_1)` where m is the slope and
  `(x_1,y_1)` is a point.

Since the question doesn't specify which form we should write the answer in, we can use any one of the forms.

Let's write the equation in slope-intercept form, as it is the most popular way to write the equation of the line.

Solving

As we already know the slope of the line, we can plug it into the formula.

y = mx + b

y = -3x + b

Now, we need to find b.

As the line passes through (3, -2), we can use its values to help solve for b.

Substitute 3 as x and -2 as y.

-2 = -3(3) + b
Multiply.

-2 = -9 + b

Add 9 to both sides.

7 = b

Substitute 7 as b in the equation.

y = -3x + 7

The equation of the line is y = -3x + 7.