It is more straightforward and requires fewer steps to find the x-intercept using slope-intercept form in this case.
Here's why:
Slope-intercept form:
The equation is already in slope-intercept form: y = -2.5x + 15.
To find the x-intercept, you simply set y to zero (the point where the line crosses the x-axis).
In this case, 0 = -2.5x + 15, solving for x gives you x = 6.
Standard form:
The equation is given in standard form: 25x + 10y = 150.
To find the x-intercept, you first need to rearrange the equation to isolate y. This involves dividing both sides by 10: 2.5x + y = 15.
Then, setting y to zero gives you 2.5x = 15, which still requires one more step: solving for x by dividing both sides by 2.5, resulting in x = 6.
Comparison:
Using slope-intercept form, finding the x-intercept required only one step of setting y to zero and solving for x.
Using standard form, it took two steps: rearranging the equation to isolate y and then setting y to zero and solving for x.
Therefore, it is more straightforward and requires fewer steps to find the x-intercept using slope-intercept form in this case.
Question
The equations y=-2.5x+15 and 25x+10y=150 represent Hanna’s music festival situation. Is it easier to find the x-intercept of the graph of the equations using slope-intercept or standard form? Explain.