Question

Find the equation of the line that satisfies the given conditions

x intercept (7,0)
slope 2

standard form
slope intercept form

Answer 1

The equation of the line with an x-intercept of (7,0) and slope 2 is y = 2x - 14 in slope-intercept form and 2x - y = 14 in standard form.

Step-by-step explanation:

To find the equation of the line that satisfies the given conditions, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. Since we know the line has an x-intercept of (7,0) and a slope of 2, we can plug these values into the slope-intercept form.

First, note that the x-intercept (7,0) means that when x is 7, y is 0. Therefore, we can use the point-slope formula to find the y-intercept. Starting with the slope-intercept form:

y = 2x + b

We substitute the x-intercept into this equation:

0 = 2(7) + b

We solve for b:

b = -14

Thus, the slope-intercept form of the equation is:

y = 2x - 14

To convert this to standard form, which is Ax + By = C, we rearrange the equation and ensure that A, B, and C are integers with A being positive:

-2x + y = -14

2x - y = 14

Therefore, the standard form of the equation is 2x - y = 14.

Answer 2

To find the equation use this form:

y - y0 = m * (x - x0)

y - 0 = 2 (x - 7)

y = 2x - 14

That is the slope intercept form

The standard form is Ax + By = C

Where A, B and C have to be integer and simplified (divided by the greatest common divisor of A, B and C).

Starting with y = 2x -14

2x - y = 14.

Tha is the standard form