Find an equation of the line that contains the following pair of points.

The equation of the line is
(Simplify your answer. Use integers or fractions for any numbers in the equation. Type your answer in slope-intercept form. Do not factor.)

Ask by Hamilton Clarke. in the United States

Dec 15,2024

Question

Find an equation of the line that contains the following pair of points.

The equation of the line is
(Simplify your answer. Use integers or fractions for any numbers in the equation. Type your answer in slope-intercept form. Do not factor.)

Ask by Hamilton Clarke. in the United States

Dec 15,2024

UpStudy AI · Accepted Answer

To find the equation of the line that passes through the points $$(4, 4)$$ and $$(1, 6)$$, we first need to calculate the slope $$m$$ of the line using the formula:

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

Here, we can assign:
- $$(x_1, y_1) = (4, 4)$$
- $$(x_2, y_2) = (1, 6)$$

Substituting these values into the slope formula:

$$
m = \frac{6 - 4}{1 - 4} = \frac{2}{-3} = -\frac{2}{3}
$$

Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:

$$
y - y_1 = m(x - x_1)
$$

We can use one of the points, say $$(4, 4)$$, and the slope $$m = -\frac{2}{3}$$:

$$
y - 4 = -\frac{2}{3}(x - 4)
$$

Now, we will simplify this equation. First, distribute the slope on the right side:

$$
y - 4 = -\frac{2}{3}x + \frac{8}{3}
$$

Next, add 4 to both sides to isolate $$y$$:

$$
y = -\frac{2}{3}x + \frac{8}{3} + 4
$$

To combine the constants, we convert 4 into a fraction with a denominator of 3:

$$
4 = \frac{12}{3}
$$

Now, we can add the fractions:

$$
y = -\frac{2}{3}x + \frac{8}{3} + \frac{12}{3} = -\frac{2}{3}x + \frac{20}{3}
$$

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

$$
\boxed{y = -\frac{2}{3}x + \frac{20}{3}}
$$
y = -2/3x + 20/3

Find an equation of the line that contains the following pair of points.

The equation of the line is
(Simplify your answer. Use integers or fractions for any numbers in the equation. Type your answer in slope-intercept form. Do not factor.)

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Find an equation of the line that contains the following pair of points. The equation of the line is (Simplify your answer. Use integers or fractions for any numbers in the equation. Type your answer in slope-intercept form. Do not factor.)

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Find an equation of the line that contains the following pair of points.

The equation of the line is
(Simplify your answer. Use integers or fractions for any numbers in the equation. Type your answer in slope-intercept form. Do not factor.)