Question

Write an equation of the line that passes through (9,8) and is parallel to the line y=-5x-4

Answer 1

▸ y = 5x - 37

Step-by-step explanation:

We are asked to write an equation for a line that:

• passes through (9,8)
• is parallel to y = 5x - 4

Parallel lines have the same slopes. So, the line that's parallel to y = 5x - 4 has the same slope as the line y = 5x - 4, which is 5. However, the y-intercepts are different.

We know the slope of the new line, but we also know the point that it passes through. So, we can use our point-slope formula:

`\boldsymbol{y-y_1=m(x-x_1)}`

Substitute our values:

`\boldsymbol{y-8=5(x-9)}`

Distribute 5:

`\boldsymbol{y-8=5x-45}`

Add 8 to both sides:

`\boldsymbol{y=5x-45+8}`

Simplify:

`\boldsymbol{y=5x-37}`

Result:

▸ y = 5x - 37

Answer 2

Answer:The equation of a line parallel to another line will have the same slope. The given line has a slope of -5. So, the line parallel to it will also have a slope of -5.

The general equation of a line is given by y=mx+c

where m is the slope and c is the y-intercept.

We know that the line passes through the point (9,8). Substituting these values into the equation gives us:

8=−5∗9+c

Solving for c, we get:

c=8+5∗9=53

So, the equation of the line that passes through (9,8) and is parallel to the line y=-5x-4 is:

y=−5x+53

Step-by-step explanation: