graph shows a line with the same y-intercept as the graph of 10x - 16y = -40?
To find the y-intercept of the graph of the given equation 10x - 16y = -40, you can set x to zero and solve for y:
10(0) - 16y = -40
-16y = -40
y = -40 / -16
y = 2.5
So, the y-intercept of the graph of the given equation is (0, 2.5).
Now, if you want to find the equation of a line that has the same y-intercept, you will look for a line where the y value is 2.5 when x is 0. The equation of a line in slope-intercept form (y = mx + b) with y-intercept b can be written as:
y = mx + 2.5
where m is the slope you choose for your new line. The value of m can be any real number; it will determine the slope of the line that shares the y-intercept with the original line. If m is different from 10/16 or -5/8 (the slope from the original equation), then the line will have a different slope but the same y-intercept.
For example, if you choose m = 1, then the equation of the new line with the same y-intercept is:
y = 1x + 2.5
which can be simplified to:
y = x + 2.5
Any line with a different slope but with "+ 2.5" as the constant in the equation will have the same y-intercept as the graph of the original equation.