Ineed to solve for x and y using linear pairs

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ginocousins06

19.10.2022

Mathematics

Answer (assuming it can be in slope-intercept form):

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

Step-by-step explanation:

When knowing the y-intercept and a slope of a line, you can write its equation in slope-intercept form, or y = mx + b format.

1) First, find the slope. Use two points from the graph. We can see that the points (0,2) and (4,5) are on the line, therefore substitute their x and y values into the slope formula $m = \frac{y_2-y_1}{x_2-x_1}$ and solve:

$m = \frac{(5)-(2)}{(4)-(0)} \\m = \frac{5-2}{4-0} \\m = \frac{3}{4}$

Thus, the slope is $\frac{3}{4}$ .

2) Next, find the y-intercept of the line by looking at the graph. The y-intercept is the point at which the line intersects the y-axis. By reading the graph, we can see that that point is (0,2), thus 2 is the y-intercept.

3) Now, using the slope-intercept formula y = mx + b , substitute the found values for the and the to write the equation of the line.

Since represents the slope, substitute $\frac{3}{4}$ in its place. Since represents the y-intercept, substitute 2 in its place. This gives the following answer and equation:

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

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