The slope-intercept form of the equation of a line that passes through point (–3, 8) is y = –y minus 3 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 8 right-parenthesis.x + 6. What is the point-slope form of the equation for this line?
you have some strange ideas about posing questions.
Your words seem to mean
y = –y - 3 = -2/3 (x+8). x + 6
but I have no idea what do do with that. Care to retype so it makes sense?
To find the point-slope form of the equation for the line passing through the point (-3, 8), we first need to understand the slope-intercept form of a linear equation and how to convert it to the point-slope form.
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Looking at the given equation, we have y = -y - 3 = (-2/3)(x + 8) + 6.
To manipulate this equation into the slope-intercept form, we can start by simplifying the expression on the right side:
y = -y - 3
y = -2/3(x + 8) + 6
Next, we can distribute the -2/3 to the terms inside the parentheses:
y = -2/3 * x - 16/3 + 6
Simplifying further:
y = -2/3 * x - 16/3 + 18/3
y = -2/3 * x + 2/3
Now we can see that the slope (m) of the line is -2/3 and the y-intercept (b) is 2/3.
To convert this equation to the point-slope form, we use the formula y - y1 = m(x - x1), where (x1, y1) is the given point.
In this case, the point is (-3, 8), so we substitute these values into the formula:
y - 8 = -2/3(x - (-3))
y - 8 = -2/3(x + 3)
This is the point-slope form of the equation for the line passing through the point (-3, 8).
To find the point-slope form of the equation for this line, we need to convert the given equation in slope-intercept form to point-slope form.
The slope-intercept form of a linear equation is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept.
From the given equation, we have:
y = -y - 3 = -2/3(x + 8) + 6
Now, let's simplify this equation:
Start by distributing -2/3 to (x + 8):
y = -2/3x - 16/3 + 6
y = -2/3x - 16/3 + 6/1
y = -2/3x - 10/3
Now, let's rearrange the equation to match the point-slope form:
y - y1 = m(x - x1)
From the given point (-3, 8), we can substitute the values of x1 and y1 into the equation:
y - 8 = -2/3(x - (-3))
y - 8 = -2/3(x + 3)
Therefore, the point-slope form of the equation for this line is: y - 8 = -2/3(x + 3)