Question

Find the equation of the line that passes through point (6, 1) with the x-intercept of 2.

Answer 1

Answer:

○ $y = \frac{1}{4}x - \frac{1}{2}$

Step-by-step explanation:

To find the equation of the line, let's first consider the points whose coordinates we have been given:

• (6, 1)

• (2, 0).

The point (2, 0) is what is called the x-intercept, which is the point where the line crosses the x-axis. This means that at this point, the y-coordinate of the line is 0.

Next, let's calculate the slope (gradient) of the line using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

where:

m = gradient,

$(x_2, y_2)$ and $(x_1, x_2)$ = points on the line.

Using the formula:

$m = \frac{1 - 0}{6 - 2}$

⇒ $m =\bf \frac{1}{4}$

Finally, now that we have two points on the line as well as the line's slope, we can use the following formula to find the equation of the line:

$\boxed{y - y_1 = m(x - x_1)}$

You can use any of the points on the line as $y_1$ and $x_1$.

Using (2, 0):

$y - 0 = \frac{1}{4}( x - 2)$

⇒ $y = \frac{1}{4}x - \frac{1}{2}$

Therefore the equation of the line is $y = \frac{1}{4}x - \frac{1}{2}$.

Learn more about point-slope form at:

brainly.com/question/15143525