Which equation represents the line that passes through the points (-3,7) and (4,10)
the point-slope form is
y-7 = (7-10)/(4+3) (x+3)
To find the equation of a line that passes through two given points, we can use the point-slope form of a linear equation. The formula for point-slope form is:
y - y₁ = m(x - x₁)
Where (x₁, y₁) are the coordinates of one point on the line, and m is the slope of the line.
First, let's find the slope (m) using the two given points (-3,7) and (4,10).
m = (y₂ - y₁) / (x₂ - x₁)
m = (10 - 7) / (4 - (-3))
m = 3 / 7
Now that we have the slope (m), we can choose one of the points, say (-3,7), and substitute its coordinates into the point-slope form equation.
y - y₁ = m(x - x₁)
y - 7 = (3/7)(x - (-3))
y - 7 = (3/7)(x + 3)
Let's simplify the equation further:
y - 7 = (3/7)(x + 3)
y - 7 = (3/7)x + 9/7
Finally, let's rearrange the equation into the slope-intercept form (y = mx + b) by isolating the y variable:
y = (3/7)x + 9/7 + 7
y = (3/7)x + 9/7 + 49/7
y = (3/7)x + 58/7
Therefore, the equation that represents the line passing through the points (-3,7) and (4,10) is y = (3/7)x + 58/7.