Find the equation of the line that has the same slope as the line through points (0,4) and (-5,7). But goes through point (-6,4)
slope = m = (7-4)/(-5-0) = ...
once you find m, replace it in the equation
y-4 = m(x+6)
arrange into the form that you are familiar with.
I mean sorry but I still don't seem to understand
What would (m) be?
Would M= Y-4/x+6??
m = (7-4)/(-5-0) = -0.6
Y = mx + b.
4 = -0.6*(6) + b, b = 7.6.
Eq: Y = -0.6x + 7.6
To find the equation of a line with the same slope as the line through the points (0,4) and (-5,7), we first need to determine the slope of that line.
The slope of a line passing through two points, (x₁,y₁) and (x₂,y₂), can be calculated using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Therefore, for the given points (0,4) and (-5,7), the slope is calculated as follows:
slope = (7 - 4) / (-5 - 0)
= 3 / -5
= -3/5
Now, we have the slope (-3/5). Next, we need to find the equation of a line with this slope that passes through the point (-6,4).
The equation of a line can be represented in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line, we'll substitute the slope (-3/5) and the coordinates of the given point (-6,4) into the equation:
4 = (-3/5)(-6) + b
Simplifying further:
4 = 18/5 + b
To solve for b, we'll isolate it by subtracting 18/5 from both sides:
4 - 18/5 = b
To simplify this, we'll convert 4 to the fraction 20/5:
20/5 - 18/5 = b
2/5 = b
Thus, the value of b is 2/5.
Now, we have the slope m = -3/5 and the y-intercept b = 2/5. Plugging these values back into the slope-intercept form, the equation of the line becomes:
y = (-3/5)x + 2/5