What is the equation in standard form of the line that has x intercept − 4 and y-intercept 3

Since the equation has the x-intercept -3 and the y-intercept -5, this means the equation goes through the points (-3,0) and (0,-5)

First lets find the slope through the points (

,) and (,)

Start with the slope formula (note: is the first point (,) and is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

So the slope is

------------------------------------------------ Now let's use the point-slope formula to find the equation of the line: ------Point-Slope Formula------

where is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Rewrite as

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

------------------------------------------------------------------------------------------------------------ Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in

form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver)

Graph of through the points (,) and (,)

Notice how the two points lie on the line. This graphically verifies our answer. Now let's convert the equation into standard form So the standard equation that x-intercept -3 and the y-intercept -5 is

When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

Video Source (08:37 mins) | Transcript

To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

Additional Resources

1. Find the y-intercept of the line:
   \({\text{y}}=-3{\text{x}}-9\)


2. Find the x-intercept of the line:
   \({\text{y}}=-4{\text{x}}+12\)


3. Find the y-intercept of the line:
   y − 9 = 3x


4. Find the x-intercept of the line:
   y + 12 = 2x


5. Find the y-intercept of the line:
   \({\text{x}}+6{\text{y}}=-24\)


6. Find the x-intercept of the line:
   \(5{\text{x}}+4{\text{y}}=-20\)