Question

Find the equation of the line described. Write your answer in standard form. With x-intercept 5 and y-intercept 3

Answer 1

To answer this question, we need to know that the x- and y-intercepts are:

• The x-intercept: (5, 0). The point where the line passes through the x-axis.

,

• The y-intercept: (0, 3). The point where the line passes through the y-axis.

To find the equation of the line, we can use the two-point form equation of the line, and then we will find the standard form of the line, which is of the form:

`Ax+By=C`

We still need to label both points:

• (5, 0) ---> x1 = 5, y1 = 0.

,

• (0, 3) ---> x2 = 0, y2 = 3.

The two-point form of the line is given by:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Then, substituting these values into this equation, we have:

`y-0=(3-0)/(0-5)(x-5)\Rightarrow y=(3)/(-5)(x-5)\Rightarrow y=-(3)/(5)(x-5)`

Then, we have:

`y=-(3)/(5)x+(3)/(5)\cdot5\Rightarrow y=-(3)/(5)x+3`

This is the slope-intercept form of the line. To find the standard form of the line, we can multiply the equation by 5 as follows:

`5(y=-(3)/(5)x+3)\Rightarrow5y=5(-(3)/(5))x+5\cdot3\Rightarrow5y=-3x+15`

Adding 3x to both sides of the equation, we have:

`5y+3x=-3x+3x+15\Rightarrow5y+3x=15`

Finally, the standard form of the line is given by 3x + 5y = 15.