write an equation in slope-intercept formof the line satisfying the given conditions: parallel to the graph of
3x-5y=7 andpasses through (0,-6)
First get the slope m of the original line by putting
3x-5y = 7
into standard y = mx + b format.
y = (3/5)x -7/5
Obviously m = 3/5. It will be the same for the new line.
The equation of the new line is
(y+6)/x = m = 3/5
Rewrite that in standard form.
To find the equation of a line parallel to the graph of 3x - 5y = 7 and passing through the point (0, -6), you can follow the steps below:
Step 1: Convert the given equation to slope-intercept form (y = mx + b).
3x - 5y = 7
-5y = -3x + 7
y = (3/5)x - 7/5
Step 2: Determine the slope of the given line.
The slope of the given line is (3/5). Since we want a line parallel to this, the parallel line will have the same slope.
Step 3: Use the slope-intercept form (y = mx + b) with the slope value and the given point (0, -6) to find the y-intercept (b).
-6 = (3/5)(0) + b
-6 = b
Step 4: Write the final equation with the slope and y-intercept.
The equation of the line parallel to 3x - 5y = 7 and passing through (0, -6) is:
y = (3/5)x - 6