What is the equation of the line that passes through the point left bracket, minus, 3, comma, 6, right bracket(−3,6) and has a slope of minus, 4−4?
The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the line passes through the point (-3,6) and has a slope of -4, we can substitute the values into the equation to find the y-intercept (b).
6 = -4(-3) + b
6 = 12 + b
6 - 12 = b
-6 = b
So, the equation of the line is y = -4x - 6.
To find the equation of a line, we need a point on the line and its slope. The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
Given that the point (-3,6) lies on the line and the slope is -4, we can substitute these values into the equation:
y = mx + b
6 = -4(-3) + b
6 = 12 + b
To isolate b, we can subtract 12 from both sides:
6 - 12 = b
-6 = b
Therefore, the value of b is -6. Now we can write the equation of the line as:
y = -4x - 6
So, the equation of the line that passes through (-3,6) with a slope of -4 is y = -4x - 6.
To find the equation of a line when given a point and the slope, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1)
Where (x1, y1) represents the given point and m represents the slope of the line.
In this case, the given point is (-3, 6) and the slope is -4. Plugging these values into the point-slope form, we get:
y - 6 = -4(x - (-3))
Simplifying the expression in the parentheses:
y - 6 = -4(x + 3)
Distributing the -4 to both terms inside the parentheses:
y - 6 = -4x - 12
We can rearrange this equation to the slope-intercept form, y = mx + b, by isolating y:
y = -4x - 12 + 6
Combining the constants:
y = -4x - 6
So, the equation of the line that passes through the point (-3, 6) with a slope of -4 is y = -4x - 6.