Final answer:
To solve linear equations given two points, calculate the slope and use one of the points to find the y-intercept. Then, express the linear relationship with the slope-intercept form y = mx + b. The resulting equation for the given points (3, 4) and (0, 5) is y = (-1/3)x + 5.
Step-by-step explanation:
To solve linear equations using two points, such as (3, 4) and (0, 5), you would first calculate the slope (m) of the line that these points dictate.
The slope is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. In this case, the slope is calculated as:
m = (Y2 - Y1) / (X2 - X1)
= (5 - 4) / (0 - 3)
= 1 / -3
= -1/3
Once we have the slope, we can use one of the points to find the y-intercept (b) using the point-slope form of a line, which is y - y1 = m(x - x1). For example, using point (3, 4) we find:
4 - y1 = (-1/3)(3 - x1)
4 = (-1/3)(3) + b
4 = -1 + b
5 = b
Now, we can write the linear equation in slope-intercept form, which is y = mx + b:
y = (-1/3)x + 5
This equation represents the linear relationship between any x and y values on this line. To visualize it, you could plot additional points using the equation and draw a line through them, just as described with the y = 9 + 3x example from the given information.