Question

What is the equation of the line that has a slope of 3 and goes through the point (-3, -5)?

a. y = 3x + 4
b. y = 3x - 4
c. y = -3x + 4
d. y = -3x - 4

Answer 1

The equation of a line with a slope of 3 that passes through the point (-3, -5) is y = 3x + 4. This is found using the slope-intercept form y = mx + b by substituting the given point and solving for the y-intercept b.

Step-by-step explanation:

The question asks for the equation of a line with a slope of 3 that passes through the point (-3, -5). To find the equation of the line, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since we already know the slope is 3 and we have a point through which the line passes, we can substitute these values into the slope-intercept form and solve for b.

Here's how we find the y-intercept (b):

1. First, we substitute the known point (-3, -5) into the equation: -5 = 3(-3) + b.
2. Then, we solve for b: -5 = -9 + b leading to b = 4.
3. The equation of the line is therefore y = 3x + 4, which matches option a in the given choices.