Question

Write an equation of the line that passes through the given point and is parallel to the given line.

(4,7),y=5x-3
can you show how you solved it please ​

Answer 1

To find the equation of a line parallel to a given line, we use the fact that parallel lines have the same slope. Using the point-slope form of a line, we can find the equation of the line that passes through (4,7) and is parallel to y=5x-3, which is y = 5x - 13.

Step-by-step explanation:

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope. The given line has a slope of 5, so the parallel line will also have a slope of 5. We can use the point-slope form of a line to find the equation.

Using the point (4,7) and the slope m=5, the equation of the line is y - y1 = m(x - x1).

Substituting the given values, we get y - 7 = 5(x - 4), which simplifies to y - 7 = 5x - 20. Rearranging the equation, we have y = 5x - 13. So, the equation of the line that passes through (4,7) and is parallel to y=5x-3 is y = 5x - 13.

Answer 2

Step-by-step explanation:

y = 5x - 3 is in slope-intercept form.

The slope of this given line is 5,

=> Parallel line will also have slope 5.

We have y = 5x + c, where c is a constant.

When x = 4, y = 7.

=> (7) = 5(4) + c, c = -13.

Therefore the answer is y = 5x - 13.