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! Let's go through each question step by step.
Question 1: Find an equation for the line with the given properties, expressed in slope-intercept form.
To find the equation of a line in slope-intercept form (y = mx + b), we need two pieces of information: the slope (m) and the y-intercept (b).
However, you haven't provided the properties of the line, so we cannot proceed without that missing information. Please provide the necessary details so that I can assist you with finding the equation.
Question 2: Find the equation of a line that is perpendicular to the line y = (1/2)x + 4 and contains the point (-3, 0).
To find the equation of a line perpendicular to another line, we need to consider the following:
1. Perpendicular lines have slopes that are negative reciprocals of each other.
2. We already have the equation of the given line y = (1/2)x + 4 in slope-intercept form, with a slope of 1/2.
To find the slope of the line perpendicular to y = (1/2)x + 4, we take the negative reciprocal of 1/2:
m_perpendicular = -1/(1/2) = -2
So, the slope of the perpendicular line is -2.
Now, we can use the point-slope form of a line to find the equation, using the given point (-3, 0) and the slope (-2):
y - y1 = m(x - x1)
Substituting the values, we have:
y - 0 = -2(x - (-3))
Simplifying further:
y = -2(x + 3)
Expanding the equation:
y = -2x - 6
Therefore, the equation of the line perpendicular to y = (1/2)x + 4 and containing the point (-3, 0) is y = -2x - 6.
I hope this explanation helps! If you have any additional questions, feel free to ask.