Final answer:
To find the equation of the line passing through the points (5, 1) and (3, 5), the slope is calculated first. The slope is -2. The equation can be written in either point-slope form (y - y1 = m(x - x1)) or slope-intercept form (y = mx + b), giving y - 1 = -2(x - 5) and y = -2x + 11, respectively.
Step-by-step explanation:
The first step in finding the equation of the line that passes through the points (5, 1) and (3, 5) is to find the slope of the line. Slope is calculated by taking the difference in y-coordinates divided by the difference in x-coordinates between the two points. In this case, the slope is (5 - 1)/(3 - 5) which simplifies to 4/-2 or -2.
Once we have the slope, we can use either the point-slope form or the slope-intercept form to find the equation. For the point-slope form, we can choose one of the given points (let's use (5, 1)) and substitute the values into the equation:
y - y1 = m(x - x1)
Substituting the values, we get y - 1 = -2(x - 5). Simplifying further, the equation becomes y - 1 = -2x + 10.
For the slope-intercept form, we substitute the slope (-2) and one of the given points (let's use (5, 1)) into the equation:
y = mx + b
Substituting the values, we get 1 = -2(5) + b. Simplifying further, the equation becomes 1 = -10 + b. Solving for b, we find that b = 11. Therefore, the equation in slope-intercept form is y = -2x + 11.
Learn more about Writing an equation given two points