for each equation tell weather its graph is a horizontal or a vertical line
y=-4
write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation
(1,3);y=3x+2
horizontal
slope is 3
y=3x+b
putin the point given, solve for b.
To determine whether the graph of an equation is a horizontal or vertical line, we can examine the form of the equation.
For the equation y = -4, we can see that there is no variable x. This indicates that the graph of this equation is a horizontal line. In general, an equation in the form y = constant will always result in a horizontal line since the value of y does not change with different values of x.
Now, let's move on to finding an equation in slope-intercept form (y = mx + b) for a line passing through the point (1,3) and parallel to the graph of y = 3x + 2.
To find the equation, we need to know that parallel lines have equal slopes. In the given equation, the slope is 3.
So, our equation will have a slope of 3. Now we can use the point-slope form of the equation of a line, which is: y - y1 = m(x - x1), where (x1, y1) represents the given point.
Substituting the values, we have:
y - 3 = 3(x - 1)
Next, we can simplify the equation:
y - 3 = 3x - 3
Lastly, rearranging the equation to the slope-intercept form, we get:
y = 3x - 3 + 3
y = 3x
Therefore, the equation in slope-intercept form is y = 3x, representing a line parallel to the graph of y = 3x + 2 and passing through the point (1,3).