Question

Graph this line:
y+3=
–
4(x+3)

Answer 1

To graph this line, we need to rearrange it into the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Starting with the given equation:
y + 3 = -4(x + 3)

Distribute -4 to both x and 3:
y + 3 = -4x - 12

Next, subtract 3 from both sides to isolate y:
y = -4x - 12 - 3
y = -4x - 15

Now we have the equation in slope-intercept form:
y = -4x - 15

The slope of this line is -4 and the y-intercept is -15.

To graph, choose a few x-values and find the corresponding y-values using the equation:

When x = 0:
y = -4(0) - 15
y = 0 - 15
y = -15

When x = 1:
y = -4(1) - 15
y = -4 - 15
y = -19

When x = -1:
y = -4(-1) - 15
y = 4 - 15
y = -11

Plot these points: (0, -15), (1, -19), and (-1, -11)

Use these points to draw a straight line. Remember that the slope is negative, so the line will be steep and slant downwards to the right.

The graph of the line y = -4x - 15 would look like this: