Write an equation of a line (in standard form) that has the same slope as the line 3x-5y=7 and the same y-intercept as the line 2y-9x=8

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have two standard form equations which we will get a slope and a y-intercept from. We will convert each to slope intercept form to get the information. We will then write a new slope-intercept equation and convert to standard form.

3x-5y=7 has the same slope as the line. Let's convert.

The slope is .

2y-9x=8 has the same y-intercept as the line. Let's convert.

The y-intercept is 4.

We take and b=4 and substitute into y=mx+b.

We now convert to standard form.

For standard form we need the coefficients of x and y to be not zero or fractions. We need integers but the coefficient of x cannot be negative. So we multiply the entire equation by -5 to clear the denominators.

picture below