I have two questions please.
1. find an equation for the line with the given properties. Express in slope-inntercept form.
2. find the equation of a line that is perpendicular to the line y=1/2x+4 and contains the point (-3,0)
please show work
Sure! I can help you with both of your questions. Let's start with the first one.
1. To find the equation for a line, we need two things: the slope (m) and the y-intercept (b). The slope-intercept form of a line is given by the equation y = mx + b.
Since you haven't provided any specific properties for the line, I'll assume you have enough information to find the equation. Let's say we have the slope (m) and the y-intercept (b) values.
Once you have the values for m and b, you can directly substitute them into the slope-intercept form equation. For example, if the slope is 2 and the y-intercept is 3, the equation would be y = 2x + 3.
If you have specific properties or additional information for the line, please provide them so that I can help you further.
Now, let's move on to the second question:
2. To find the equation of a line that is perpendicular to a given line, you need to first determine the negative reciprocal of the given line's slope, and then use a given point to find the y-intercept.
Given the line y = 1/2x + 4, the slope of this line is 1/2. To find the negative reciprocal, invert the fraction and change the sign. Therefore, the negative reciprocal of 1/2 is -2.
Now we have the slope of the perpendicular line, which is -2. We also have a point (-3, 0) that the line needs to pass through.
To find the equation, we'll use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values into the equation, we get: y - 0 = -2(x - (-3)).
Simplifying further, we have: y = -2(x + 3).
So, the equation of the line that is perpendicular to y = 1/2x + 4 and passes through (-3, 0) is y = -2x - 6.
I hope this helps! Let me know if you have any further questions.